Mathematics and statistics

Receptor model

A receptor model is a statistical method that estimates pollution source contributions from measured concentrations at a site, working backward from the data rather than from emissions.

Reciprocity law

A reciprocity law is a theorem of number theory relating solvability of congruences modulo different primes, exemplified by quadratic reciprocity, first proved by Gauss in 1796.

The Reconstruction conjecture, also known as the Kelly–Ulam conjecture, is an unsolved problem in graph theory asserting that every graph on at least three vertices is determined by its vertex-deleted subgraphs.

Recreational mathematics

Recreational mathematics, also called mathematical recreations, is mathematics pursued for enjoyment rather than application, covering puzzles, games, paradoxes, magic tricks, and topological curiosities such as Möbius bands.

Rectangle

A rectangle is a quadrilateral with four right angles, a special parallelogram with equal, parallel opposite sides and equal diagonals; its area is length times width.

Rectangular function

The rectangular function, also called the rect or gate function, equals 1 on an interval centered at zero and 0 elsewhere; its Fourier transform is the sinc function.

Rectangular hyperbola

A rectangular hyperbola, also called an equilateral or right hyperbola, is a hyperbola whose two asymptotes are perpendicular, equivalent to equal semi-axes (a = b) and giving it the fixed eccentricity √2.

Recurrence quantification analysis

Recurrence quantification analysis (RQA) is a nonlinear time-series method that quantifies a recurrence plot into measures such as determinism, laminarity, and entropy, introduced in the 1990s.

Recurrence relation

A recurrence relation, also called a recurrence equation, defines each term of a sequence as a function of earlier ones; with initial values, like the Fibonacci recurrence, it determines the sequence uniquely.

Recursion

Recursion, also called recursivity, is the process of defining or solving something in terms of smaller instances of itself, as when a function invokes itself on simpler sub-problems.

Recursion theorem (Dedekind)

The Dedekind recursion theorem, proved by Richard Dedekind in 1888, guarantees that a function defined by recursion on the natural numbers exists and is unique.

Recursion theorem fixed point

In computability theory, a recursion theorem fixed point is a program index n with the same partial function as its transform, φn = φf(n), guaranteed by Kleene's second recursion theorem.

Recursive Bayesian estimation

Recursive Bayesian estimation, also known as Bayesian or Bayes filtering, sequentially estimates a system's hidden state through prediction and update steps, with the Kalman and particle filters as best-known forms.

Recursive language

A recursive language, also known as a decidable or Turing-decidable language, is a formal language decidable by a Turing machine that halts on every input, finite or not.

Recursive largest first algorithm

The recursive largest first algorithm is a greedy graph coloring heuristic, introduced by Frank Leighton in 1979, that builds each color class as an independent set.

Recursive least squares filter

The recursive least squares (RLS) filter, or RLS algorithm, is an adaptive filter that recursively minimizes weighted squared error, converging faster than LMS at higher computational cost per step.

Recursive partitioning

Recursive partitioning is a statistical method that builds classification and regression models by repeatedly splitting a dataset into smaller subgroups, producing a binary tree whose leaves carry predictions.

Recursively enumerable language

A recursively enumerable language, also called a Turing-recognizable language, is a formal language accepted by some Turing machine, which may run forever on strings outside it.

RecycleUnits

RecycleUnits, also written Recycle-Units, is a linear-time algorithm that shrinks SAT solvers' resolution proofs and their unsatisfiable cores, introduced by IBM Haifa and Technion researchers in 2008.

Redescending M-estimator

A redescending M-estimator is a robust statistical estimator whose influence function rises near the data's center and falls to zero for large residuals, completely rejecting extreme outliers instead of merely down-weighting them.

Reduce (computer algebra system)

REDUCE is a portable, general-purpose computer algebra system begun by Anthony C. Hearn at Stanford in 1963 for physics calculations, and free, open-source software under a modified BSD license since 2008.

Reduced basis method

The reduced basis method, also known as reduced basis, is a model order reduction technique for parametrized partial differential equations, first introduced in the late 1970s.

Reduced ring

A reduced ring is a ring containing no nonzero nilpotent elements, so x squared equaling zero forces x to be zero; examples include every integral domain and Boolean ring.

Reduced word

A reduced word, also called a reduced expression, is a shortest expression for an element of a Coxeter group as a product of simple reflections, with its common length the element's length.

Reduced-rank regression

Reduced-rank regression (RRR) is a multivariate statistical method that models many correlated responses as linear functions of predictors through a low-rank coefficient matrix, used in econometrics, biology, and neuroscience.

Reductive group

A reductive group, or reductive algebraic group, is an algebraic group whose unipotent radical is trivial; examples include GL, SL, SO, and Sp, central to the Langlands program.

Redundancy (engineering)

Redundancy in engineering is the use of more than one independent means to do a job, so one failure does not stop the system; the gain requires independent failures.

Redundancy analysis

Redundancy analysis (RDA), also called reduced-rank regression, is a constrained ordination method introduced by C. R. Rao in 1964 that relates response variables to explanatory variables through regression followed by PCA.

Reeb vector field

A Reeb vector field is the unique vector field associated to a contact form on an odd-dimensional manifold, defined by α(R) = 1 and ιR dα = 0.